Luckily for you, it would seem Applejack was considerate enough to not let you start entirely from scratch when it comes to catching the Apple-Crab, and she has recently, with Applebloom's help, constructed what she reckons is a pretty fearsome trap for the elusive beastie. It appears to be an extremely large grid of squares, a hundred by a hundred by your count, with several arrows pointing in all different directions, along with walls of several revolving doors.
So how, exactly, does this implausibly elaborate device function, you ask? Applejack proudly explains. The trap is to be baited with several apples, and when the crab attempts to nibble on one, it will instantly activate the device and force the crab to move. The arrows on each of the squares will move the crab in the same direction as that arrow, after which, once the crab has left that square, the arrow will rotate by ninety degrees: if it's pointing north, it will move the crab north and then change its arrow to face east, and then if the crab should visit that same square again, it will be forced to move east, and the square with that arrow will rotate again to face south, and so on.
Such a device is necessary as the Apple-Crab must remain in almost constant motion, lest it gain its bearings long enough to use its venomous and acidic bubbles that they naturally possess to simply melt their way out of the trap and wreak havoc on the orchards once again. The only catch, however, is that in the event that the crab hits an edge square and it points towards the wall of the trap, nothing will happen, and the crab will be able to escape. However, she remains decently confident that such a trap will be for the most part largely unescapable, and her crop shall be saved.
Is she right though, you think. Is this trap actually foolproof, and if not, how is the best way to carefully and deliberately destroy her hopes and dreams?
The obvious answer is true.
While the other 64 squares can be used as many times as we want, the 32 on the walls gets at best 3 uses, with the 4th time pointing towards the wall. The 4 corners are even worse, they only get used twice safely, with use 3 pointing towards one of its 2 wall.
The real question is, will the trap last long enough to come up with a more permanent solution.
A quick fix is to have the squares next to wall to point away from said wall, and don't change the way the arrow points, but I don't think we will have enough time to fix all 36 arrows.
Unfortunately, this trap is no good - it can always be escaped.
Each of the corner squares can be used at most twice before they point outwards and become escape points. Similarly, each of the edge squares can be used at most three times before they point outwards and become escape points. The center squares do not appear to have any such restrictions, and can be used as many times as we want. Now, let's assume that the crab does get trapped in some sort of infinite loop. Since each of the corner/edge squares can only be used a certain number of times, there has to be some point at which an edge square is used for the final time. After this, the crab can only move throughout the center 98x98 squares, without ever escaping to the outer ring.
If this sounds familiar to you, well, it should, because we've just created exactly the same problem we were trying to solve in the first place, only with a smaller grid - 98x98 instead of 100x100. From here, we can use exactly the same steps we did before to confine the crab further, to a 96x96 grid, then a 94x94 grid, and so on and so forth, until we get all the way down to a 2x2 grid. At that point, there are no center squares, so the crab must escape it. That means it will keep escaping the 2x2 grid until it eventually escapes the 4x4 grid, then the 6x6 grid, and so on all the way up to the initial 100x100 grid (and even beyond, if Applejack thinks just making a bigger grid will be enough to trap it.